Recuperator



July 8, 1930'. v l D. B. HENDRYX i? `Iris/.9,994

RECUPERATOR original Filed Jan. 2e. 192s s sheets-sheet. 1

July 8, 1930. D. B. HENDRYX RECUPERATOH Original Filed Jan. 26, 1928 3 SheetssSheet 2 IN VENTOR oOOOoOQ/@O 5. ab

l Z0 5 ZZ M MATTORNEY RECUPERATOR original FiledJan. 26, 192s 5 sheets-sheet s lNvENToR /z l' ffendyx BY I (LMU-c.. ATTORNEY Patented July 8, 19304` UNiTi-:DsTA'TEs DWIGHT D. HDNDRYIQ or BRADFORD, PENNsYLvANraQAssiGimR TIQYHANLEY coin-j PANY, 0F BRADFORD, EENNSYLVANIA, CRPORATION OF PENNSYLVANIA REcUriiRAroR Appiicaitlimiiiefi January 26, i928, serial Naaiaei. aexiewediwtay 27, 1930.

VMy invention consists in the novel features hereinafter described, reference being had tothe accompanying drawings which show one embodiment of the invention Vselected by me for' purposes of illustration, and the saidinvention is fully disclosed in the following `description and claims,

My invention Aconsists in a novel recuperapassage'of the respective fluids throughthe recuperator, and designed primarily for the purpose of reclaiming the heat inv waste or exhaust gases from a heating process or from' `a heating furnace, or furnaces, for example,

the exhaust gases from the firing zone or other portion of a tunnel kiln and using t-he reclaimed heat for the purpose ofheating. air kept out of contact,` or admiXture with the exhaust gases, it being understood that the i'ecuperator may be employed for vany other n purposes for which 'it may be o'r is found tobe advantageous. According toiriy inven'v f tion the separate passages are provided forA conducting Lthe heating fluid, and the fluid to be heated through the recuperator out of contact with each other, said passages being of any desired form,`or arrangement, and having heat transferring portions separating said passages, and exposed on opposite sides to the heating fluid and the fluid to be heated. The passages for heating fluid, which necessarily becomes cooled as it passes through the iecuperator, and therefore reduced in volume, diminish in cross-sectional area, or capacity, inisubstantial proportion to the reduction of volume ofthe heating fluid, there by maintaining a substantially uniformkvelocity of the heating fluid through the recuperator. Tlie'passages for the fluid toibe.

hea-ted, the volume ofwhich increases during Yits passage through the recuperator, are increased in cross-sectional area or capacity,

in substantial proportion to the increase of volume due to the' expansion of the heated fluid. This construction result-s in a high rate ofheat transfer; and the .prevention of the formation of a stagnant lilm Vof heating fluid on thesurfaces of the passages for the heating fluid and fluidto be heated, and resultsnin exceptionallyfhigh eflici'ency in the operation ofthe recupverator. The heat con .V

ducting portions of .the passages may be formed of'metal or other suitable material,- as silicon carbide,for example, and I findit convenient 'Kto'employ tubular passages of niet-al or silicon carbide, or other suitable mafV terial, as portions of the passages 'for one" fluid, and located within'passages for they other,'inlwhicli case the variation of the ca-v pacity of the passages of which said tubes,

form a part can be conveniently accom;v

plished by varying the number of tubes or the diameter of the `tubes,'or both, as desired.

My invention also comprehends certain defluid Vandthe heated fluid is secured, together with an extremely inexpensivel and economif cal construction reducing the initial cost, to` v gether With a low power consumption vin,

moving the fluids through the recuperator. In the accompanying' drawings,

Fig. l represents a horizontal sectional view of a recuperator embodying my i1iven! tion. n

Fig. .2 represents a central vertical sectional view of t-he saine. Y

Fig. represents a transverse vertical sectionalL View on the line 3-3 of Fig. 2.

Fig.k t is a viewsimilar to Fig. 2, illus# tir-ating a slight modification.y

Fig. 5 is a horizontal sectional view of a recuperator. embodying a slight modification n heat insulatingwmaterial,indicated at lb and f' 2b. l/Vithin the side walls, l, l, are located header walls, 4,4., preferably formed lof fire brick,v and in this instance extending parallel and longitudinally of the recuperat'or7 forming a central passage indicated at 5, for

ice i one of the fluids,.as the heating fluid, in this- 1nsta11cewaste gases from a furnace, or fury n'aces, said passage beingofv uniform Width,

but gradually decreasing in height from4 the entranceend of the passage,-5, (at right' in Figs.4 '1 and 2) vtothe exit or discharge end,

(at the left `in Said figures; Y Between eachl header" Wall and the adjacent side Wall of the recuperatorisa space Which is divided by,

transverseivertically. dSpOSd Partitions, Gf

into a.plurality ofheaders, indicated at 7', 8,

- 9, 10, 11 andr12, the transverse.partition, 6,

on one side of the recuperator being :staggered With respect to those onthe otherv side Vv`'i5V .Y the heating fluid,VK are placed banks of tubes of thechamber-i. Across the passage, `5j, for

of heatA conductingmaterial, indicated at 13,

v121, 15,16 and,17,'communicatingyvvith@the i headersonf yopposite sidesof, the passage, 5,1 "five banks beingshoivn,"althoughanydesired Y number Qofl banksmay be" employed." VThese y banksjfoftb'es effect Vcommuni'cation between,V

the headersjon opposite sideso'ffthe "firing i f chamberand'form therewith,thepassages for .the vother fluid, as thefluid to be heated, in this instanceair, ispreferably introduced` by meanso'f a pipe, orpassage,18, into 1 the header, 17.5,@,These'headers and tubes Vare sofarrangedthat the "fluidpa'ssing therethrough will be" conducted successively t throughihe headers, s, 9,10, i1, and i2, and

discharged from the lattei` through asuitable pipe, or passage, 19, traversingf all of the tufbesof each bank. I As' the air or other fluid tobeheated will increase lin volunfie in passingfthrough the recuperator 'the capacityof the communicating banks ofA tubes" is increased substantially in proportion tov the 1ncrease volume eected'by. the heat of the heating fluid, or gases', passing'through the passage, 5, and this preferably accomplished as clearl' indicatedffin Fig. 2, by increasing .y

. the num er 'of tubes in the different banks longitudinally'of the recuperatonthe bank, 13, contai'ningfthe greatest'number f tubes and being subjected to `the highest heat of the heating `fluid at theentrance end of the passage,y 5. .d I `prefer to employ tubes of silicon carbide, ormetal, orlOther suitable heat con- 'sok Vducting material, Whichcan b e conveniently set Lfluid tight'in the header Walls, 4, 2l, so as to preventthe escapeof the heated fluid into the heating fluid, or vice versa. `By increasing thenumber oftubes of equallength and area in the banks', the capacity of the passages p fonthe heatedyfluid are graduallyincreased,

Y endof the recuperator at vvv'hic'hthe heating. f

While the 'cross-sectional area-of the tubes re` mains" uniform and facilitates the uniform transferof heat from the heating fluid to YJche heated fluid. 1

,The side 'Wallsandlheadervvalls. fof the re' cuperator decrease in vertical height .from ,the

fluid entersftbv'vard the end'fifoin Vwhich they @are dishafsedes ,Shownrnilii'e and the passage, y5, and headers, `7-12 inclusive, are

closed at their upper ends by aflat arch, or

roof, as illustrated in 3, comprising sections, 20, 21'and v22, of fire brick, over Which is preferably placed a layer of heat insulating material, 23. Ipreferto form the flat arch in` three transverse sections, as shown, the' central section, 20, covering the passage, .5, for 'the heating fluid, and resting upon the header Walls, 4, 4, the headersbeing covered by the 1 separate lateral portions, 21 f and 2 2, A,of ,the

arch, which preferably rest upon the header Walls and the adj acent lateral Walls, 1, 1, of

The' insulating material, 23,'assists in sealing the-arch, While the transthe recuperator.

verselydivided. construction of the ,arch aplloivsfor slight variations in vertical expan-` sion `ofthe header Walls"k and lateral Walls Without subjectii'ig` the roof or arch to inj urious strain, Which might be the case if the arch sections ezte'nded entirely acrossrthe recupera-tor Vfrom oneexterior tvall to the other and incontact v vith the header Walls, which especially at the entrance'end arefsubjected to very lhigh temperatures from the heating fluid. This construction also prevents any leakage ofV the heatingfluid intothe heated fluid,jo`r viceversa, asin case any leakage occurs, it Will ordinarily be to orfrom the pas# mospliere. v h

It isaavell knoivnfact that for efficient heat transfer froma fluidl to a solid, the velocity of the `fluid past the Vsurface'of the solid mustbesuflicient to'preven't `the forma! sagesofone 'or other of said fluids and the attion of astagnant filmof fluid on the surfacel ofthe solid.: This is particularly true in `re gard to gases, which are poor conductors of heat. V'llhiisfin a recuperator of the tube type,

it is desirable for eliicient operation that the 'Velocityof the heatingfiuid and also the heated fluid be high enough to prevent the formationVV of a stagnant vfilm of fluid on the exterior or the interior of the tubes, but not high enough to A'ca usfean excessivedrop in pressure, which Would necessitate additional power to mYe :the'fluids through their respective passages. A

IA definite Weight of heating `Huid, as flue gas for example, fromafurnace at a temperature 'of`15000` F., Would have about -tvvice the volume that the same ,amount of gas would have when leaving the recuperator after being cooled to atemperature of 500o F. If the crossffsecti'onal area, or capacity, of the spaces able them to givelup theirV heat thereto and 7.a

i, nantfilin ofgas will form on the eXterior of to Ythe lfluid vto lbe heated within the salme, and the power `required to move the gases will be very-high. AtI the kdischarge end of the recuperator where the heating gases leave, their velocity will be so low, by reason of the decreasein volumel by cooling, ythat a stagtheheat conducting surfaces, or tubes, and the rate of heat transferred will be correspondingly lowered. A. corresponding effect will also be produced on the heated'fluid, thus reducing materially the efficiency of Athe recuperator, as the heated -fluid is constantly increasing in temperature and volr urne.' `In other words, in theordinary recuperator construction in .which the passages for the heating fluid andthe fluid to be heated are of substantially uniform capacity throughout, the lvelocities are ltoo 'low -at one end and too high at the other, and the power required to pass thje'fluid through their respective passages withinthev recuperator is unnecessarily great. In accordance with my invention as hereinbefore described, the pas'-` sages for the heating fluid gradually decrease in capacity in substantial proportion with the decrease in volume dueto cooling, while the passages for the heated fluid increase in capacity in substantial proportion with the increase in volume, so that a substantially uniform velocity of both the heatl maximum efficiency. The recuperator can be built on a flat slab foundation, indicatedat 2a? for example, without complicated underground foundation structures, arches or iiues. Y It is not essential that the sectional flat arch, or roof or the recuperator should be enclosed with insulatingkmatei'ial, 23, and this may be omitted,-and the sections, 20, 21 and 22,' laid in the form of slabs Without mortar, permitting them to be removed when;

desired for cleaning out, as there .is practically no opportunity` for leakage of one fluid into the other, or vice versa, in my construction. The air, or f1uid,.to ber heated passing through the recuperator is usually lunder apressure lhigher than that of the atmosphere, while the heating fluid, or flue gas, is usually under suction, that is, at a pressure lower thanv atmospheric,L therefore,

any. leakage which is likely tooccur., at the roof, or arch, will be between the atmosphere andthe heati'ngfluid,y or between the atmosphere and the fluid to be heated, andvnotbetween the heating fluid and the fluid to be heated, or vice versa.v f

I have shown Vas my preferred .construction inl-lig. 1, 2 and 8,'an arrangement in which `the. vpassages .for the heating fluid are decreasedin height while their width remains uniform and with the tubesof .conductingy material arrangedin horizontal position, but this is not essential. The passage for the .heating gases can be placed vertically, with crosssectional area increasing either up# wardly ordownwardly, and the tubes may be placed horizontally.` The Vtubes cangalso be placed vertically with the passagesfor heatingrgases horizontal.` I prefer thehori- Zoiital arrangement of tubes, however, as it veliminates underground flues, which would be practically necessitated if the tubes were;

Placedv vertical. It will also be understood that the heatingiluid may be passed through the tubes and the `air or other fluid to be heated may be passed through the passage, 5, in the reverse direction to thatshown in the arrows in Figs, 1, 2 and 3, if desired, but I prefer the arrangement shown in which a horizontalk flow of bo'thfairand gases is obtained, and the air to be heated passes through the tubes. It is also to beV understoodthvat while the recuperator shown and described is areferabl used b assino theV heatinwiiuid throughthepassage, 5,'aiid the fluidto be `heats-cl through the headers and tubesin the respective directions indicated by the arrows,

the fluid to. be' heated may `be passed through the passage, 5 inthe opposite. direction to4 that indicated by thearrows, and the heat'- ing fluid may be passed through the headers andvtubesialso in the opposite direction' to `thatindicated bythe'arrows, if desired.

In F 4L. I have shown a slight modificaion of my invention, in which similar parts are indicated by the same reference numer-l als, with the addition of 100 to avoid repeti tion, and these parts neednot be againl described. n

In this modification, Ihave shown a construction in which the increased capacity of the banks of tubes is obtained by increasing the/ diameter ofthe ktubes themselves inthe `different banks withoutincreasing materials ioo ly their number, thus the tubes of the several banks,.117, 116, 11st and 113, are increased in diameter in a direction toward the Y entering end of the passage, 5, for the heating fluid.v The operation of this form of recuperator will be precisely 'the same as that vpreviously described, and need not be repeated. u

It will be understood that in the operation of the recuperator, the passage, 5, willv ordinarily he connected with a conduit, or passage, indicated at 25, leading from a furn nace or furnaces, or other sources `of waste, or other highly -ieated gaseous products, and

after said products have passed through the recuperator they are conductedlaway by a suitable pipe, or conduit, 26. On account ofthe A undesirabilityV of VSubj ecting a i fan,

vother `forcing means, to the Vsaidl products when very vhighly heated, it is preferable `Ato provide' the `power for moving, the heating i fluid through the y,recuperattn by suction,and

this may lbeconveniently accomplished by connecting the conduit, 26, with' a" suitable source of suction, as a suction fan, or a stack.

Itl is customary to move the fluid to beheated" through' the recuperator byimeans of a forcingdevice,.as` a fan, or blower, which may be` connected with inlet pipe, 18,'fas the :fluid to be heated leavesthe frecuperator fatsuch j high temperature ,thatjit lwouldbe inadvis-v `able to passit through laisuction fan. 'VVhere 'the temperatures permit, "however, a1 suction` ff fan could be connectedywith outlet pipe, 19,

for the fluid tofbe heated`,f"and the heating huid could be withdrawn from its sourceby .any suitablemeansland forced through thel "'conduit, 25,1`through therecuperator, .within- VY- tlre scope ofiny invention. i y

Wherefit is desired to construct recuperators vof `very large Capacity and to-avoid the use, of tubes of :heat conducting material, of excessive length, I may provide a plurality of longitudinal' passages in the recuperator decreasing `in capacity `from one endl to the other-V and each providedwitha series of banks oftubes of heat conducting'material *constructed Vto` increase the capacityof` said l banks in the o osite direction :lonffitudinal- PP e - hereinbefore: described, 1n c0n]unct1on wlth headers on opposite sides of said passages,

'ly of the recuperator, either by increasing* the number of' tubes inthesucces'slv'e banks',-`

or by increasing the diameter of the tubes, as

communicating with the tubes, so that the heating fluid and thefiuid to be heated'will be divided either before entering thfe recuperator or during its passage therethrough.

InFig. 5, I haveillustrated apartial plan View ofone form of recuperator embodying my invention in which this feature isxcarried out, the'corresponding parts to those lil` lustr'atedginFigs;` 1, 2 and 3 being indicated by the Vsame .reference ch'ara'cters with the `addition of 200.. In. this instance I'have 1 yshown two ,longitudinal passages, 205 and 205,1separated by centrallylocated headers,

207,V 2,09 and 211, separated from each other by transverse walls, 206, and communicating with the inner ends of banks of tubes,

indicated at 213, 214, 215 and 216, extending i across theapassage 205, and valso communicating with the `inner ends of'banks of tubes, 213, 214, 215 and216, extending across the i passage, 205a, the outer` ends 'of each set ofbanks of tubes communicating with exterior headers, 208, 210, A2082`1 and 210?-,*as vclearly `indicated-in Fig. 5, it being understood that 4 inthis .instance a vertical longitudinalsec? y tion througheachpassage,l205 and 20521, will ,be substantially identical with the cross section illustrated inAFi'gL12,that is to say,`the

ters Patent is `hei-ghi; ofY Said passages will 'decrease-inthe direction of the"arrowsfa?,in-Fig;l 5, while the blanks of tubes-will increasein number in the Y opposite direction;l The centrally located-headers,f207, 209a`nd2`11, are preferably made of double thegcapacity of the exterior headers, as shown f In this'construction one lof the: fluids, which 'may befor example i erator in thedirections` indicated by the 0ther arrows'in Fig. fandpassing outfrom the -header,'211. Obviously the heating fluid could'be passed throughthe tubes andthe .fluid to be heated* through the tubes and headers, and the fluid to be heated could "be passed'through the passages, 205: and 205, by

reversingthedirection of movement olf-both fluids, if Vthis were desirable.` Itv will also be understood that any desired number of longitudinal passages' for one fluid contain- Aing banks of `tubes for the other fluid 4and constructedand operati-ngjas hereinbefore described, couldbe employed'. I Y

In theV specication and claims, I have referred to the heating fluid as indicating the highly heated fluid as the waste furnace gases, etc., from which heat is tobe recovered, .and the fluid to which the heat is to be transmitted from the heating Huid, I have termed the fluid to be heated. y 'y WhatI claimand desire to secure by Letl. A recuperator provided with a passagefor the heating fluidtherethrough, and

provided with passages for a fluid to be heated, through the recuperator, said passages comprising tubular heat conducting' `members located within said passage, the` capacity of the passages for the fluid to be heated increasing between the point of entrance of said fluid and thepoint of eductionV thereof substantially in proportion to the .increase in volumeV of said fluid to be heated by reason ofthe increase in temperature thereof, whereby the lvelocity of the fluid to be heated may be maintained throughout the recuperator, and the formation of a stagnant film of said fluid on the interior of the tubularconducting members is prevented. Y 2'. A recuperator provided with a passage Vfor the heating fluid gradually decreasing in passes throughV the-banks of ltubes andextelrior headers on the otherside of the'recupl capacity substantially in proportion ,to the decrease in `volume of said luid'due to the cooling thereof, and passages for the fluid to f be heated including heat conducting tubular members located within said first mentioned passage increasing in capacity between the point of entrance of said fluid to be heatedV heated, for conduct-ing said fluids respectively through the recuperator in opposite directions,

one of said passages decreasing in capacity and the other increasing in capacity in the opposite direction, the conducting passage for one of said fluids including tubular heat conducting portions located within thepassage for the other Huid, whereby the velocity of each fluid may be maintained substantially constant throughout therecuperator, and the formation of a stagnant lrn of one fluid on the exterior of said tubular portions, and of the other fluid on the interior of saidv tubular portions is prevented. v

4. A recuperator provided with a centrall located passage decreasing in capacity from one end to the other, headers located on opposite sides of said passage., and banks of heat conducting tubes connecting said headers in series and extending transversely'of the first mentionedpassage. f

5. A recuperator provided with a centrally located passage decreasing in capacity from one end to the other, headers located on oppo-v site sides of said passage,`and banks of heat conducting tubes connecting said headers in series and extending transversely of the iirst mentioned passage, said banks of tubular connections increasing in capacity longitudinally of said central passage inthe. same direc-U tion as the increase in capacity of said passage, said central passage and the passages formed by said headers and tubular connect'i'dns being` provided respectively with means for passing a heating Huid and a fluid tobe heated therethrough in opposite directions.

6. A recuperator provided with a centrally located passage having vinduction and eduction connections, headers Vlocated upon opposite sides of said central passage, banks of heat conducting tubularv connections extending between said headers, and having por Y tions of conducting material within said central passage and connecting said headers in series, induction and eduction connections for the passages formed by, said headers and tubular connections, the capacity of said tu-` fbularheat conducting connections beinifincreased gradually between theinductionand v eduction'connections substantially in proportion with the'incrjease in voluinenof the -iuidil .passing therethrough, whereby the velocity; of

said fluidfnliayfbe'. Vmaintainsd substantially uniform' throughout the recuperator, and the i .formation of a stagnantl film of `fluidwithin prevented. i

vlocated passage having induction and educsaid 'tubular heat lconducting connections is tiony connections, headers; located. upon opn posite sides of said central passage, a plurality of series vof tubular connections, of heat'conducting materialconnecting said headers in series, and extending across said first mentioned passage at different points longitudinallythereof, induction and eduction connections for vthepassages formed by,l said headers and, tubular connections, the num-l ber of tubular connections in the several series increasing, in aV direction longitudinally of said` centralfpassage substantially in proportion to the increase vin volume. of the fluid passing therethroughl,v

ly located passage having induction and veduc- 8. A .recuperator'provided with a centrali tion connectionsfheaders located upon opposite sides of said central passage, a plurality of seriesv of'tubular. connections, ofheat conducting. material y connecting said y headers in series, and extending across said Y iirst mentioned passage at different points :longitudinally thereof, induction and .eduction connectionsfor the passages formed by saidV headers .and tubular connections, the number'of tubular connectionsin the several series increasing in a direction longitudinally of said. central passagej substantially yin 1 proportion'to vthe, increase in volume of the fluid passing'therethrough, said central passage `decreasing in capacity longitudinally .thereof ina direction opposite totheincrease of `oapacity vofsaidfseriesV of tubular connections.

'9. recuperator providedvwitha support#` ingbase, side and end'walls, parallel header walls Yextending. longitudinallyl of the recup,-E

eratorl and space dfroin'pthe exterior wallsyfv transverse.. partitions extending fromveach header wall to the adjacentY exteriorwallfto' provide a centrallongitudinal passage and ay plurality of headers on each side thereof, the partition .wallsfo'n one -side'of said central passage being staggered with respect to those on the opposite side, a series of tubular confvnections of heat conducting material extend-v .ing from each header to a header on the opposite side of said central passage and con'-V necting saidheaders inseries, saidconnections having portions extending across said central passage, and an archconstruct-ion covering said headers and said central and sealing the same. l0. A recuperator'provided with. a suppassage,

I f f 1,769,994

. porting; base,V side and end` Walls, parallel y header' walls"extendinglongitudinally of 'the 1 o reuperator:V and 4sp'aed from the exterior f ,walls, ftransverse partitionsgextending `Vfrom j f5 eaeh headerlwallto theadjaoent exterior Wall i i to providea .central longitudinal passage and Y `V i i e apluraltyof headersfnfeach side thereof, the, j i

vpartition Walls on* one side of said central lpassage being staggered Withrespeet to those t I0 on Athe opposite'side, aA series of tubiilar oon-V neetionsvof heat conducting Inaterialextend* ingfrorn eaohheader to a header on the op posite sidel of 'said Centralv passage andv yoonf nectingsaidffheaders inseries, saidxconneeo 15't1on'shav1ng portions-extendingacross said `central passage, an archoonstruetion having portions covering said" central passageand o supported bythe header Walls, and separate portions vcovering said headers andrsiripport- `goed" bythe header Walls and adjacent exterior Y wa11s@" ,v Y f `11. `"A.reeuperat'orprovided"with a sup- Y `porting base; side and endjwalls, parallel `header-:Wallsjextending longitudinally of the g zerecn'perator and fspaoedr Vfrein theJV V exterior Walls,` transverse partitions Vextending lfrom eachheader Wall to the Vadja'eent exterior Wall'. Y i

to` provide a Centralv longitudinal passage and i i atplurality `of headers'on' each. Side thereof, L V30 'thepartitionwalls on oneside ofsaidcentral 1 passage being staggeneiil With'respect to those i on the opposite side',` aj series Vof tubular `conv neotionsof heat Conducting material extendingfromeach header toaheader on the 0p- 35 posite lsideofsaidieentral passage and oonneoting said headers 1n series, .said eonneo` tionshavingportions extendingaoross said 'eentra'lpavssaga'anarch construction-having portionsy covering "said eentralxpassage, and to` snp'ported` bythe header Walls', and separate 'I portions eoveringsaidheaders'and supported lby the;l header Walls and adjacent exterior VYWalls,said' centralfpassage `decreasingV inv ,heiglitfrom oneend 'of the reeliperator to the 4:5 other to Vary `the capacity thereof-siibstan-V ti ally 'inpropvo'rtion .to the change in `volume ofther fluid passingtherethronghandthe .i

-` o said,tubular-connections'between the headers f Qonvlthf-i` opposite :sides ofisaidpassageincreasvvi vloll-in'gin "capacity inv the opposite direction,

" loI'lgitudinally ofthe reouperator f sbstan- Y tialiy 4in proportion to the jehange in volume y Vofthe'vliqnid'passingtherethrough. f 1 Y In `testimony hereof f1 a'ilixjmy signature.` 

